That is always the case in the predator-prey dependence cycle. It's not really a behavior that is determined by the animal, but, rather, an uncontrolled biological response.

From the predator perspective: If there's an abundance of resources, predators will show up and their populations will increase, and when the resource dwindles, so too will the family size decrease and predators will leave. Some animals react biologically much quicker than other species: take rats, for example. This same response is seen in human poplulations throughout the world.

From a prey perspective: If there's an abundance of resources to sustain a larger population, the population will grow to capacity until the resources dwindle and populations decrease: take Bison, for example. Predatory stresses also cause this fluctuation in family size. In some species the family size decreases in response to predation and other species the family size increases to overcome predation.

Food controls the populations.